What is a proper bankroll in terms of big-bets and buy-ins? Is it different for lower stakes vs higher stakes? What is the minimum for starting at a new stake vs playing regularly at a stake? I have found very little information on bankroll and bankroll management for limit hold'em on the internet and what I have found has varied among sources

For a sustainable roll, you'll probably want 500 BB.
If you can regularly replenish your roll through non-poker means, 100 BB is enough.

If you're shot-taking at a higher stake, I would say a good amount is 500 BB at your current stakes + 100 BB at new stakes.

In 15 years of online short handed mostly 15/30+

The number of times I would have been broke with a 500BB role is probably like 15?

The number of times I would have been broke with a 750BB role is probably 4?

The number of times I would have been broke with a 1000BB role is 1.

The largest one which was like 1200 BB was like 10 years ago.

And then the pressure of living expenses. I'm pretty nitty. Even tho technically all of my money is my bankroll I would be incredibly stressed out personally if I didn't have some living expenses set aside basically. It's not always possible obviously but something I've worked extra hard on making a point of...cause man can poker be rough for hundreds of thousands of hands. Then again sometimes you run hot for a long while.

BRM always starts with "what's my win rate and how hard would it be to replace a lost BR?" Nobody can give you a generic answer that's correct, because your WR in the game is key.

Are you playing for a living and withdrawing from your BR? Do you just not want to replenish but could easily afford to do so?

So, first question. What is your WR in the game you want to play, and over what sample did you achieve this?

What stakes are you planning to play? How many hours have your played at those stakes so far? Are you losing? Breakeven? Winning?

Your skill level along with playing style is important regarding variance and how much of a buffer you need.

Are you actively doing things to improve your game?

I think I fyp.

Nobody plays perfect and there are different ways to play equally bad poker, so yes, playing "style" matters.

Perhaps you can provide an example of different "playing styles" because I'm not even sure what that means. I get that those who play equally good or equally bad can create unnecessary variance in neutral EV situations. But the most optimal way to decrease variance afaik is to increase win rate. Period.

Do you think this sort of variance is normal at Full Ring live games? Online games are just so much tougher imo. I am a BR nit but I am not convinced this type of variance exists in live FR. I currently am keeping 750BB for live 20/40 at Canterbury. I think in this game it is maybe on the excessive side but I'm curios what other people think.

Now if I was playing a bigger/tougher game where there are significantly less fish I would be more inclined to move up to the 1000bb mark but I think my edge is significant enough to have a low RoR at 750.

As for "Playing Style" I am under the impression that LAG play comes with more variance. The lags I know, who play pretty well, always seem to have much larger swings than me (I play TAG). I believe this to be especially true if your post flop game is not extremely good or if you are prone to tilting when running bad since you will have more opportunities to leak chips with a LAG style.

I'm pretty sure this is a fallacy. A good LAG shouldn't be playing hands that are unprofitable for the situation. So the "L" in LAG simply means pushing the outer boundaries of profitability.

Sure. But reducing hand or session swings should never be the objective imo. You could TAG it up by folding the marginally profitable hands that a good LAG plays and bring your variance to zero for those hands. But your risk of ruin will INCREASE with each fraction of a big bet you give up in your win rate. A good LAG making 1.5BB/hr in a live game will have larger swings per hand and possibly per session, but will always be able to get by with less of a bankroll than a .5BB/hr. TAG.

This is my understanding at least, and why I'm kind of grunching over all this talk about player styles. I'm sure someone will correct me if I'm wrong.

As for tilting when running bad... Yeah, don't do that.

A LAG winning 1bb/hr will have much higher variance and bigger swings long and short term than a TAG winning 1bb/hr. Both are equally bad at poker in terms of long term expectation.

you shouldn't use the word "variance" like that. it's incorrect. if your session swings are higher but your high winrate means your probability of having a large downswing is lower, you still have higher, not lower variance. there's no such thing as "overall variance".

With the current canterbury 20/40 situation 750BB is plenty. Other things would be in play if a person busted a 750BB role there. The game is just sooooo soft so often.

Live poker just sucks so hard because it takes so much longer to reach any sort of volume...and even after a number of years the sample is still pretty small. Be the chosen one...mgm style you know?

FWIW, these online games do require a much larger roll, since they're usually much tougher (so your max downswing will be much higher when you're a 0.5 BB / 100 winner than a 2.5 BB / 100 winner).

I'd say 500 is fine for live FT grinding. 750 is wicked safe.

I view variance as statistical noise. Both experts and novices alike can and will reach the outskirts of the bell curve on each side for short term periods if they play long enough. All I'm maintaining here is that the best thing one can do to reduce their risk of ruin and bankroll requirement is not to worry about playing style (whatever that is), but to improve their win rate. Also, a 1.5BB/hr player figures to suffer thru fewer and less prolonged downswings than a 1BB/hr player regardless of "playing style".

Agree 100% if you're not living off of it. Monthly nuts come often and at 20/40 are a lot of bets.

Personally I wouldn't feel comfortable as a 20/40 player with 40k to my name and a 4k nut. There's nothing wrong with it I'd just be trying to put in extra hours building some more padding for a long stretch of not winning.

//edit I just realized 4k nut is prob a tad high for a 20/40 grinder but it can't be too far off.

This is also true.

Basically as a "semi-pro" (so you play to win $, but you can just quit if it's not working out), 500 BB is just fine. But as a pro, you really should be subtracting your expenses out as a function of your hours played. Like 125 hours a month played and 3k a month in expenses, playing 20/40? That's 0.6 bets an hour from your win rate. So if you're a 2.5 BB/100 winner, you're really only "adding" 0.7 bets to you roll per 100.

And Win Rate and Bankroll requirements are inversely related using this formula. So 500 is probably plenty as a semi-pro, since at 2.5 BB/100 w/ 0 BB/100 withdraw & 19 BB/100 standard deviation, risk of ruin is around 0.1%. However, if you have the same win rate as a pro but a 1.8 BB/100 withdraw, your RoR shoots up to 14.4% (which is totally unacceptable). For the same RoR as the prior guy, you'd need an almost 1800 BB bankroll.

So yeah after doing the math, you're 100% right BK. As a pro, you probably need a 1500+ BB Bankroll unless your game is an absolute joke, you're a world beater, you can manage off a small self-imposed salary, or you have income from other sources.

Hi Kevin:

It depends how you do it. If you improve your win rate through improving your ability to read hands (and this includes interpreting your opponent’s range) expect your variance to go down.

If you improve your win rate through adding high risk plays then expect your variance to rise.

Best wishes,
Mason

This would only be accurate if it led to folding more. And yes, you'll be able to make soul read folds that lower your variance. But in reality if you become a better hand reader you're going to be able play more hands. Adding additional hands is going to increase your variance more than making the occasional hero fold is going to decrease it.

(If your contention is that better post flop reads will lead to lower variance if you don't adjust your preflop range for your increased ability, then sure.)

Generally, when gambling, and this includes poker, those additional plays that experts use to obtain a higher win rate will increase your variance and I showed this in my Gambling Theory book over 30 years ago. But there are a few exceptions and reading hands well is one of them. Also, for those questioning this, just pretend the cards were marked which would give perfect reading ability, an extremely high win rate, and a low variance, and yes you would be able to play some additional hands.

Best wishes,
Mason

If you had marked cards with perfect reading ability you could play 72s in the small blind against an UTG raise with AA profitably. You could play probably 3 times as many hands profitably as you would otherwise (depending on how aggressive the game is, especially preflop). Your variance on the hands you would play anyway would go down, but overall your variance would skyrocket. Of course that would hardly matter because you'd win every session.

I think there's a big misconception here. There's a relationship between the standard deviation and your win rate that determines an acceptable bankroll size. Suppose you're right that it is okay to play 72o against a pair of aces if you had perfect reading ability and all these additional hands do drive your variance up (and remember the square root of the variance is the standard deviation). It doesn't meant you need a bigger bankroll and that's because at the same time your win rate has gone up.

What I find frustrating whenever this stuff comes up is that the correct answers have been around for over 30 years. For instance, a bankroll formula that I use is:

BR = (9)(Var)/(4)(WR)

which puts you at about a 1 percent risk providing your variance and win rate is always the same every time you play. There are other formulas around that will give you similar results (and you can see Post #17 above for another example). But the important thing to notice here is that both variance and win rate are part of the equation.

So if you do something that both increases your win rate and your standard deviation (or variance), does it send your required bankroll up or down. The answer is that it depends how much each is increased.

Best wishes,
Mason

lets say a Nit and a Lag end up after a year with the same win rate. Doesn't it seem more likely that the Lag might have exceed a "300 bet" bankroll than the Nit? Therefore the Lag may require a bigger bankroll.

I don't think anybody is worried about playing one style or another.

Hi Mason,

Would you know if this is the same formula used in StatKing (which I purchased in 1998 and still use to this day)?

I admit my use of the word variance was sloppy according to stinkypete. My overall point was that increasing win rate (no matter how you do so) is a more important metric when it comes to reducing risk of ruin than standard deviation. I jumped itt in response to a comment made about reducing a buffer zone.

In my haste I was imprecise in my assertion that an expert LAG will suffer less downswings. In fact, I'm sure an expert LAG will have a lot more -50BB sessions than a lesser skilled TAG. However, I still maintain the expert LAG will suffer less prolonged downswings (in other words, will go less time before making new money)...

A live game player with a 1BB/hr win rate and a 10BB/hr standard deviation has around a .25% chance of going broke starting with a 300 BB bankroll, whereas a 2BB/hr winning LAG with a 12BB/hr standard deviation has around a .02%. So increasing win rate by 1 big bet even while increasing standard deviation by 2BBs is clearly better. I maintain my overall point is correct. Assuming you have an adequate starting bankroll and are in it for the long haul, the best thing you can do to decrease risk of ruin is to increase win rate rather than worry about standard deviation (variance).

I'd definitely be more willing to back a player with a higher win rate and higher standard deviation (more variance) over a player with a lower standard deviation (less variance) with a lower win rate any day unless of course, the difference in win rate was minimal.